Answers
4) Where the hypotenuse is 100 and the adjacent side is x and α = 45°, the x = 70.71
5) Where the opposite side is 100, and α = 45°, the hypotenuse is 141.42
6) Where the hypotenuse is 88 and β = 45°, x (the opposite side) is 62.23
7) Therefore, the length of each leg of the 45°-45°-90° triangle with a hypotenuse length of 26 is approximately 18.33 units.
8) Therefore, the approximate length of the hypotenuse of the 45°-45°-90° triangle with a leg length of 50 centimeters is 70.71cm.
9) Where the Base is 11 and α = 30°, Hypothenus (x) = 22 and Opposite (y) = 19.05
10) Where the hypotenuse is 8√3, and β = 45°, opposite (x) = 11.99 and adjacent (y) = 6.93
11) Where the adjacent is 5√3 and α = 30°, opposite (x) = 14.99 and Hypothenus (y) = 17.32
12) where hypotenuse = 30, and the β = 60°, the adjacent (x) = 15 and the opposite (y) = 25.98
13) where opposite is 36.372 and the β = 60°, the hypothenus (x) = 41.99 and the adjacent (y) = 20.99
14) where the hypotenuse is 90.316 and β = 60°, the opposite (x) = 78.22 and the adjacent (y) is 45.16
15) An equilateral triangle has an altitude length of 27 feet, and the length of a side is 15.588 feet.
16) the length of a side of the equilateral triangle is 22 feet.
What is the explanation for the above results?The basic rule applied here (from 4-14) is the principle of SOHCAHTOA.
The principle of SOHCAHTOA is a mnemonic device used to remember the three basic trigonometric ratios in a right triangle:
Sine (sin) = opposite/hypotenuse
Cosine (cos) = adjacent/hypotenuse
Tangent (tan) = opposite/adjacent
In SOHCAHTOA, each letter represents one of the ratios:
"S" stands for sine, which relates the opposite side to the hypotenuse.
"O" stands for opposite, which is the side opposite to the angle of interest in the right triangle.
"H" stands for the hypotenuse, which is the longest side of the right triangle and is opposite to the right angle.
"C" stands for cosine, which relates the adjacent side to the hypotenuse.
"A" stands for adjacent, which is the side adjacent to the angle of interest in the right triangle.
"T" stands for the tangent, which relates the opposite side to the adjacent side.
By using SOHCAHTOA, we can quickly and easily find any of the three basic trigonometric ratios, given two sides of a right triangle and an angle.
In 4) This is an example of a right triangle, where one of the angles is 90 degrees. In a right triangle, the side opposite the 90-degree angle is called the hypotenuse, while the other two sides are called the adjacent and opposite sides.
In this case, the hypotenuse is given as 100 units, and the angle between the hypotenuse and adjacent side (x) is given as 45 degrees. To find the length of the adjacent side, we can use the trigonometric function cosine, which relates the adjacent side to the hypotenuse and the angle between them:
cos(α) = adjacent/hypotenuse
Substituting the given values, we get:
cos(45°) = x/100
Simplifying, we get:
x = 100 * cos(45°)
Using the identity cos(45°) = √2/2, we get:
x = 100 * √2/2
Simplifying further, we get:
x = 50√2
To find the approximate value of x in decimal form, we can use a calculator or approximate the value of √2 as 1.414. Then, we get:
x ≈ 50 * 1.414 = 70.71
Therefore, x is approximately equal to 70.71 units.
In 8) Where we needed to find the length of the hypotenuse of a 45°-45°-90° triangle with a leg length of 50 centimeters.
In a 45°-45°-90° triangle, the two legs are congruent, and the length of the hypotenuse is √2 times the length of each leg.
Therefore, if one leg of the triangle has a length of 50 centimeters, then the other leg also has a length of 50 centimeters, and the hypotenuse has a length of:
hypotenuse length = leg length x √2
hypotenuse length = 50 cm x √2
To simplify the expression, we can multiply the numerator and denominator of the fraction by √2:
hypotenuse length = 50 cm x √2 x √2 ÷ √2
hypotenuse length = 50 cm x 2 ÷ √2
hypotenuse length = 100 cm ÷ √2
To rationalize the denominator, we can multiply the numerator and denominator of the fraction by √2:
hypotenuse length = 100 cm ÷ √2 x √2 ÷ √2
hypotenuse length = 100√2 ÷ 2
hypotenuse length = 50√2
Therefore, the length of the hypotenuse of the 45°-45°-90° triangle with a leg length of 50 centimeters is 50√2 centimeters or 70.71cm.
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Related Questions
y=2/5+2 how to get the x intercept
Answers
Answer:
Step-by-step explanation:
The equation you provided, y = 2/5 + 2, appears to be missing the variable x. Assuming you meant y = 2/5x + 2, here's how you can find the x-intercept:
To find the x-intercept, we need to find the value of x when y = 0. This is because the x-intercept is the point on the graph where the line crosses the x-axis, and at that point, the y-coordinate is always 0.
So, we can set y = 0 in the equation:
0 = 2/5x + 2
Subtracting 2 from both sides:
-2 = 2/5x
Multiplying both sides by 5/2:
-5/2 = x
Therefore, the x-intercept is at the point (-5/2, 0).
Jayden throws a ball up in the air. The graph below shows the height of the ball h in feet after t seconds. Find the interval for which the ball's height is increasing.
Answers
The intervals during which the ball's height is increasing are: [0, 2.5] and
[5, 7.5]
What is an intervals?In a graph, an interval represents a range of values along the x-axis or y-axis. It is a continuous segment of the axis between two points, often used to indicate a particular range of values or a specific time period.
Since the graph represents the height of the ball h in feet after t seconds, we can find the interval during which the ball's height is increasing by examining the slope of the graph.
If the slope of the graph is positive, the height of the ball is increasing. If the slope is negative, the height of the ball is decreasing.
Looking at the graph, we can see that the slope of the graph is positive between approximately 0 and 2.5 seconds, and between approximately 5 and 7.5 seconds.
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I need help with please
Answers
Answer:
C
Step-by-step explanation:
You want to identify the set of ordered pairs corresponding to the given pattern definitions.
Start atThe x-pattern starts at 2.
The y-pattern starts at 0.
The first (x, y) ordered pair is (2, 0). This matches answer choice C.
__
Additional comment
The x-rule tells you the sequence is ...
2, 2+6 = 8, 8+6 = 14, 14+6 = 20 . . . . . {2, 8, 14, 20}
The y-rule tells you the sequence is ...
0, 0+5 = 5, 5+5 = 10, 10+5 = 15 . . . . . {0, 5, 10, 15}
Then the (x, y) pairs are ...
(2, 0), (8, 5), (14, 10), (20, 15)
Note that when X and Y are the variables involved, we conventionally use the ordered pair (x, y). When other variables are involved, the ordered pair may be different, not always alphabetic order.
Generally, the independent variable is listed first. Here, neither depends on the other, so that criterion does not apply. Listing X first here is also suggested by the fact that the X pattern rule is defined first.
If the 8th term of an A.P is twice the 4th term and the sum of the first terms is 47. find the five common difference
Answers
If the 8th term of an A.P is twice the 4th term and the sum of the first terms is 47. the five common difference is 3.
How to find the five common difference?Let the first term be "a" and the common difference be "d".
The 4th term of the AP is: a + 3d
The 8th term of the AP is: a + 7d
We know that the 8th term is twice the 4th term, so:
a + 7d = 2(a + 3d)
Simplifying and solving for "a", we get:
a = d
Substituting this value of "a" in the sum of the first terms, we get:
47 = (5/2)(2a + 4d)
47 = 5(a + 2d)
9.4 = a + 2d
Substituting the value of "a" from above, we get:
9.4 = 3d
d = 3.13333
d = 3 (approximately )
Therefore, the common difference (d) is approximately 3.
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I need help with this IXL special right triangles
Answers
Answer:
Step-by-step explanation:
m = 30
10√3 · √3 = 10·3 = 30
The density of the object is equal to the quotient of its mass, m, and its volume, v . An object has a density of 8 grams per liter and a volume of 16 liters. What is its mass in grams
Answers
Answer:
the formula for density is:
density = mass/volume
We know that the density of the object is 8 grams per liter, and its volume is 16 liters. We can use this information to solve for the mass:
density = mass/volume
8 g/L = mass/16 L
To solve for the mass, we can cross-multiply and simplify:
8 g/L * 16 L = mass
128 g = mass
Therefore, the mass of the object is 128 grams.
Help me! I need help with my homewor!
Answers
Answer:
Area of shaded region= 1142.96mm²
Step-by-step explanation:
•First calculate the Area covered by the interior circle.
•To calculate the Area of the exterior circle first add the two radii to get the radius from the centre of the interior circle to the circumference of the exterior circle.
•Use the calculated radius to calculate the Area covered from the centre to the circumference of the exterior circle.
•Now subtract the Area of the interior circle from the area covered by the bigger circle to get the Area of the shaded region.
Answer:
1141.76
Step-by-step explanation:
To solve for the area of the entire circle, we must first solve for the radius. Adding 6 and 14 will get us the total radius of the circle.
6 + 14 = 20Therefore, the radius of the entire circle is 20.
The expression you can use to solve for the area of a circle is:
Area = π × radius²Inserting the radius into the expression:
Area = π × 20²Therefore, the area of the entire circle is 400π.
If there is a hole in the circle in the shape of a circle, we must subtract the area of that hole to find the area of the shaded region.
Inserting 6 into the expression to solve for area:
Area = π × 6²Therefore, the area of the hole is 36π.
Now, we need to subtract the area of the gap from the area of the entire circle.
400π - 36π = 364πBecause π is approximately equal to 3.14, we can calculate an approximate value for 364π by multiplying 364 by 3.14. This gives us:
364 × 3.14 = 1141.76.Therefore, the area of the shaded region is [tex]1141.76^{2}[/tex]
A school has 500 students. The principal is to pick 30 students at random from the school to go to the Rose Bowl. How can this be done using a random-number table?
Answers
The way the principal can use a random - number table to pick 30 students from the school is explained below.
How to use a random number table ?To use a random-number table to select 30 students at random from a school of 500 students, the principal should :
Assign a unique number from 1 to 500 to each student in the school.Choose a starting point on the random-number table and begin reading the digits in pairs from left to right.Ignore any pairs that are outside the range of 01 to 50 (since there are 50 students per page).Whenever the principal encounters a pair of digits that falls within the range of 01 to 50, record the corresponding student number.Repeat steps 3 and 4 until you have recorded 30 student numbers.Check that there are no duplicates in the list of selected students.This method ensures that every student has an equal chance of being selected.
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state of each triangle is acute, obtuse, or right show work
Answers
The triangle can be classified as follow:
15: obtuse
16: right
How to know if a triangle is acute based on side lengths?To classify the triangle as acute, obtuse, or right, follow the following steps:
1. Calculate the sum of squares of the two smaller sides.
2. Compare it to the square of the longest side.
3. If the sum is greater, your triangle is acute. If they are equal, your triangle is right. If the sum is less, your triangle is obtuse.
No. 15
10² + (2√39)² = 256
18² = 324
256 < 324 (obtuse)
No. 16
11² + (2√19)² = 197
(√197)² = 197
197 = 197 (right)
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Suppose the demand and supply of beer are modeled by the two following functions:
Q = -57P + 364
Q = 25P + 26
What is the equilibrium quantity of beer? Round your answer to two places after the decimal point (0.01).
Answers
Therefore , the solution of the given problem of unitary method comes out to be $240 which will cover the cost of the new motorbike.
What is an unitary method?The task can be completed by multiplying the data gathered using this type of nanosection along with two individuals variable who utilized the unilateral strategy. In essence, this signifies that perhaps the designated entity is defined or the colour of both mass production is skipped whenever a wanted item occurs. For forty pens, a variable charge of Inr ($1.01) could have been required.
Here,
The quantity supplied and the quantity requested are equal when there is equilibrium. As a result, we can equalise the two formulae and find the equilibrium quantity:
=> -57P + 364 = 25P + 26
=> 82P = 338
=> P = 4.12
We can use either equation to determine the equilibrium amount now that we know the equilibrium price. Use the supply calculation as an example:
=> Q = 25P + 26
=> Q = 25(4.12) + 26
=> Q = 129.5
So, rounded to two decimal places, the equilibrium amount of beer is roughly 129.5.
=> $60 + $180 = $240
which will cover the cost of the new motorbike.
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x/15 = h make x the subject
Answers
Answer:
To make "x" the subject of the equation, we can isolate it on one side of the equation by multiplying both sides by 15:
x/15 = h
Multiplying both sides by 15 gives:
x = 15h
The equation in terms of "x" is x = 15h.
Step-by-step explanation:
a retailer sold bat at 25% profit
Answers
Answer:
25% Profit = CP of 5 bats = 5x W
Step-by-step explanation:
I will mark you brainiest!
In completing the following proof, which of the following statements should be included?
Given: regular ΔDAF; midpoints B, C, E; ∠DBE ≅ ∠FCE
Prove: DB ≅ FC
A) CCPTC
B) CPCTC
C) CSATC
D) CASTC
Answers
Answer:
B) CPCTC (stands for Corresponding Parts of Congruent Triangles are Congruent) should be included in the proof. This statement is necessary to show that ΔDBE ≅ ΔFCE, which then allows us to conclude that DB ≅ FC.
Step-by-step explanation:
What are the coordinates of the point that is of the way from G to F?
OA. (3,2)
OB. (5,-2)
O C. (1.5, 3)
OD. (4.5, -3)
4
6
2
-6 -4-2 0
ON
-2
-4
-6
Ty
F
2
4
6
G
X
Answers
The coordinates of the point that is halfway between G (2,4) and F (6,-6) is (4, -2).
What is coordinate?Coordinate is a pair of numbers that represents a position on a two-dimensional plane. Coordinates are usually written in the form (x, y), with the x-coordinate representing a position along the horizontal axis, and the y-coordinate representing a position along the vertical axis. Coordinates can also be used to represent positions on a three-dimensional plane in the form (x, y, z). These coordinates can be used to pinpoint a specific location or to describe the shape of a figure on a graph.
This can be calculated by taking the average of the x coordinates (2 + 6 = 8/2 = 4) and the average of the y coordinates (4 - 6 = -2/2 = -2).
Therefore, the point is (4, -2).
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!!! Please quickly need an answer!!!!
Car A and car B set off from the same point to travel the same journey. Car A sets off three minutes before car B. If car A travels at 60 km/h and car B travels at 70 km/h, how many kilometres from the starting point will the two cars draw level?
Answers
The two cars will draw level at a distance of 12 kilometers from the starting point, taking their speed and into consideration, as further explained below.
How to find the distanceSince both cars are traveling towards the same destination, the distance between them will decrease over time until they draw level. Let's call the distance between the starting point and the meeting point "d" kilometers. We can use the formula:
distance = rate × time
Since car A has a three-minute head start, car B will have to travel for three minutes less than car A. Let's call the time it takes for car B to catch up to car A "t" hours. Then:
time for car A = t + 3/60 hours
time for car B = t hours
We want to find the distance between the starting point and the meeting point, which is the same for both cars. So we can set up an equation based on their distances:
distance traveled by car A = distance traveled by car B
(rate for car A) × (time for car A) = (rate for car B) × (time for car B)
60 × (t + 3/60) = 70 × t
3 = 10t
t = 3/10 hours
Now that we know the time it takes for car B to catch up to car A, we can use either car's rate and time to find the distance between the starting point and the meeting point. Let's use car A's rate and time:
distance = rate × time
distance = 60 × (t + 3/60)
distance = 60 × (3/10 + 1/20)
distance = 60 × (4/20)
distance = 12 kilometers
Therefore, the two cars will meet 12 kilometers from the starting point.
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1, a 36 foot tree cast an 18 foot Shadow at the
Same time that a mail box carts a 4 foot shadow
how tall is the mail box
Answers
Answer:
We can use the concept of proportions to solve this problem. We know that the ratio of the height of the tree to the length of its shadow is the same as the ratio of the height of the mailbox to the length of its shadow.
Let's call the height of the mailbox "x". Then, we can set up the proportion:
height of tree / length of tree's shadow = height of mailbox / length of mailbox's shadow
Plugging in the values we know, we get:
36 / 18 = x / 4
Simplifying the left side of the equation, we get:
2 = x / 4
To solve for x, we can multiply both sides of the equation by 4:
8 = x
Therefore, the mailbox is 8 feet tall.
Step-by-step explanation:
Answer:
Height of mail box = 8 ft
Step-by-step explanation:
Given information,
→ 18 ft shadow is formed by a 36 ft tree.
→ A mail box casts 4 foot shadow.
Now we have to,
→ Find the height of the mail box.
Let us assume that,
→ Height of mail box = h
Forming the equation,
→ 36/18 = h/4
Then the value of h will be,
→ 36/18 = h/4
→ h/4 = 36/18
→ h/4 = 2
→ h = 2 × 4
→ [ h = 8 ft ]
Hence, the value of h is 8.
345.61489 rounded to the nearest ten- thousandth
Answers
Answer: 345.6149
Step-by-step explanation:
Answer:
345.6149
Step-by-step explanation:
Which expression does not have the same value as −2+3×65 ?
Answers
The expression that does not have the same value as -2 + 3×65 is 3×(65-2) which evaluates to 183, the correct option is D.
The expression -2 + 3×65 represents a mathematical calculation that involves the operations of addition and multiplication. The order of operations dictates that multiplication should be done before addition, so we start by multiplying 3 and 65 and then adding the result to -2.
The value of -2 + 3×65 is 193.
we need to evaluate each expression and compare it to 193.
Option A: 3×65 - 2 = 193
Option B: (3-2)×65 = 65
Option C: 65×3 - 2 = 193
Option D: 3×(65-2) = 183
expression that does not have the same value as -2 + 3×65 is option D: 3×(65-2) which evaluates to 183.
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The complete question is :
Which expression does not have the same value as −2+3×65?
Option A: 3×65 - 2 = 193
Option B: (3-2)×65 = 65
Option C: 65×3 - 2 = 193
Option D: 3×(65-2) = 183
QUESTION 1 The number of elements in sets A and B are shown in Figure 1.0. If n(A) = n(B) find: (a) x (b) n(A) (c) n(B) (d) n(AUB) 2x 4xx+5 Figure 1.0 10 marks
Answers
Answer:
From the given figure, we can write the following equations:
n(A) = 2x + 4
n(B) = x + 5
n(A∪B) = n(A) + n(B) - n(A∩B)
Since we are given that n(A) = n(B), we can substitute the expressions for n(A) and n(B) to get:
2x + 4 = x + 5
x = 1
(a) x = 1
(b) n(A) = 2x + 4 = 2(1) + 4 = 6
(c) n(B) = x + 5 = 1 + 5 = 6
(d) n(A∪B) = n(A) + n(B) - n(A∩B)
We still need to find n(A∩B) to calculate n(A∪B). Looking at the figure, we can see that there are 2 elements that are common to both A and B. Therefore,
n(A∩B) = 2
Substituting this value, we get:
n(A∪B) = n(A) + n(B) - n(A∩B) = 6 + 6 - 2 = 10
Therefore, (d) n(A∪B) = 10.
Step-by-step explanation:
Critical Thinking Question (5 pts.)
(You may use the back of the page to write your answer if needed). Here is a case-study for you to solve. Use what you learned
about blood types and Rhesus factor to solve this situation.
Two friends, Mike and Jake were returning late at night from a club in the same car. Suddenly, Mike, who was driving, lost control of
the car and they crashed into a big tree. Mike ended up with only a few bruises and scratches, but Jake got hurt.
Jake had internal bleeding and was taken to a hospital, but he lost a lot of blood and needed a blood transfusion. Mike, feeling
responsible for his friend's condition, wanted to donate blood to his friend. Both Mike and Jake had blood type O. So, in the ER, Mike
gave 2 pints of blood to Jake.
Two weeks later, Jake became anemic. So, Mike, being a good friend, decided to give blood again. However, after the second
transfusion, Jake went into an anaphylactic shock (severe immune response) and almost died.
What, do you think, was the problem here? Your answer should have two parts:
1. Explain, what happened in Jake's body after the first blood transfusion - why did he become anemic so soon after the transfusion?
(hint: it's not from bleeding)
2. Explain, what happened after the second blood transfusion - why did Jake go into an anaphylactic shock?
Answers
1.Jake became anemic after the first blood transfusion because his body reacted to the foreign antigens.
2.He went into an anaphylactic shock after the second transfusion due to an even stronger allergic reaction.
1. After the first blood transfusion, Jake became anemic because he was given type O blood, which is not compatible with his own blood type. Incompatible blood transfusions occur when a person is given blood that carries a different antigen than the one they have. In this case, Jake was given type O blood, which carries both the A and B antigens, while Jake’s own blood carries the Rh antigen. Therefore, Jake’s body reacted to the foreign antigens and created antibodies to fight against them. This reaction caused Jake to become equation anemic, as his body was not able to absorb the oxygen from the transfused blood.
2. After the second blood transfusion, Jake went into an anaphylactic shock because he was given type O blood, which carries both the A and B antigens, while Jake’s own blood carries the Rh antigen. Since Jake’s body had already created antibodies to fight against the foreign antigens, when it was exposed to the same foreign antigens a second time, his body reacted with an even stronger immune response. This reaction caused Jake to go into an anaphylactic shock. In other words, the second transfusion caused an allergic reaction in Jake’s body, which was much more severe than the allergic reaction caused by the first transfusion.
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HOW TO TAKE OUT HCF BY PRIME FACTORISATION
Answers
Therefore , Highest Common Factor (HCF) of two or more numbers by prime factorisation method can be done by following below given steps
What is an unitary method?This generally recognized ease, preexisting variables, and any necessary elements from the initial Diocesan customizable query may all be used to complete the job. Consequently, you might be given another chance to use the item. Otherwise, important impacts on algorithmic statistics will vanish.
Here,
To find the Highest Common Factor (HCF) of two or more numbers by prime factorisation method, follow these steps:
Express each number as a product of prime factors.
Identify the common prime factors among the numbers.
Take the product of the common prime factors. This product will be the HCF of the given numbers.
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A scientist compares the weights of strawberries from two different groups. The difference between the means of the weights for the two different groups is –10 grams. The scientist uses simulations to create a randomization distribution to try to determine the likelihood that the results happened by chance. The histogram represents the results of the 1,000 trials from the simulations.
Histogram. differences in means from random grouping.
According to the randomization distribution, is the difference in means due to chance or the group from which the measurements were made? Explain your reasoning.
Type your response in the space below.
A botanist is studying the research question, “Do seeds from a common plant take longer to germinate at 72 degrees Fahrenheit or at 75 degrees Fahrenheit?” They design an experiment in which they select 20 seeds and assign those seeds to 2 groups of 10 seeds each at random. The seeds in the first group are placed in an environment that is held at a constant temperature of 72 degrees Fahrenheit, and the seeds in the second group are placed in an environment that is held at a constant temperature of 75 degrees Fahrenheit. The germination times, in days, for each group are displayed in the table.
group 1 days to germinate group 2 days to germinate
14 14
14 13
14 14
13 14
13 13
14 13
15 14
14 14
14 15
15 13
The mean germination time for group 1 is 14 days, and the mean germination time for group 2 is 13.7 days.
a. How could the botanist get a randomization distribution to compare the two groups?
Type your response in the space below.
b. How would the botanist use the randomization distribution to determine whether the difference between the mean germination time for group 1 and the mean germination time for group 2 is due to chance?
Type your response in the space below.
Noah rolls a standard number cube 10 times and adds the values to get a sum of 28. Is that unusually low? Clare simulates rolling the number cube 10 times on a computer and adds the values. She repeats that process 100 times and creates a histogram of the results.
Histogram from 22 to 48 by 2’s. Sum of 10 rolls. Height of each bar is 1, 3, 4, 9, 9, 11, 16, 14, 12, 10, 5, 5, 1.
a. Based on the histogram, does 28 seem unusually low?
Select the correct choice.
A YesYes
B NoNo
Explain your reasoning.
Type your response in the space below.
b. The mean of Clare’s simulations is a sum of 35, and the standard deviation is 5.72. Using a normal distribution as an approximation of this distribution, what is the probability that a person would roll a sum less than 28? Round your answer to the nearest hundredth.
Type your answer in the box below.
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Answers
Answer: According to the histogram, a sum of 28 is not unusually low. The bar representing a sum of 28 has a height of 9, which is relatively high compared to some of the other bars. Additionally, the histogram is roughly symmetric, so a sum of 28 is not far from the mean of the distribution.
To find the probability that a person would roll a sum less than 28, we can standardize the value using the formula z = (x - mu) / sigma, where x is the sum of 28, mu is the mean of 35, and sigma is the standard deviation of 5.72.
z = (28 - 35) / 5.72 = -1.22
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than -1.22 is approximately 0.1112, or 11.12%. Therefore, there is about an 11.12% chance that a person would roll a sum less than 28.
Step-by-step explanation:
At a recent baseball game of 5,000 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Mustard Chili
63 27 60
Based on the data in this sample, how many of the people in attendance would prefer chili on a hot dog?
900
2,000
2,100
4,000
Answers
Answer:
The answer to your problem is, A. 900
Step-by-step explanation:
How we would need to find it:
To determine the number of people who would prefer mustard on a hot dog, we need to use the proportion of people in the sample who prefer mustard and apply it to the total number of people in attendance.
27/150 = 0.18
Next, estimate the number of people who prefer mustard in the entire population of 5,000 attendees we can multiply/x this proportion by the total number of attendees:
0.18 x 5,000 = 900
Thus the answer to your problem is, A. 900
Joanna went school supply shopping. She spent $23.89 on notebooks and pencils. Notebooks cost $1.87 each and pencils cost $1.08 each. She bought a total of 17 notebooks and pencils. How many of each did she buy?
Answers
Answer: She
bought a total of 5 notebooks and 13 pencils.
Step-by-step explanation:
Plot the following points and join them together and describe what you get, (1₁-1), (2,1), (3, 3), (4.5) (5.7)
Answers
Answer:
A positive line
Step-by-step explanation:
Answer:
Step-by-step explanation:
you get a straight line with a slope = 2
the line slants up and to the right
it passes through the y axis at the point (0, -3)
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answers
The equations that can be used to solve for y, the length of the room are: y² - 5y - 750 = 0 , (y - 30)(y + 25) = 0 , y(y - 5) + 750 = 0
Define the term equation?An equation is a mathematical statement that asserts the equality of two expressions, often with variables and constants.
To solve for y, we can use the same equation we used for x, since y represents the length of the room. Therefore, the equation we can use to solve for y is:
y² - 5y - 750 = 0
This equation can be factored as (y - 30)(y + 25) = 0, which gives us two solutions: y = 30 or y = -25. However, since the length of a room cannot be negative, the only valid solution is y = 30.
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Please help ASPA
Graph the functions on the same coordinate axis.
f(x)=-2x+1
g(x)=x²-2x-3
What are the solutions to the system of equations?
Select each correct answer.
(-2, -3)
(-2,5)
(2, -3)
(2,5)
(2, 3)
Answers
Answer: (2,-3) and (-2,5)
Step-by-step explanation:
Let us graph the two equations one by one.
If we compare this equation with the slope intercept form of a line which is given as we see that m = -1 and c =1
Hence the slope of the line is -2 and the y intercept is 1.
Hence one point through which it is passing is (0,1) .
Let us find another point by putting x = 1 and solving it for y Let us find another point by putting x = 2 and solving it for y Hence the another point will be (2,-3)Let us find another point by putting x = -2 and solving it for y Hence the another point will be (-2,5)Now we have two points (0,1) ,(1,-1) , (2,-3) and (-2,5) we joint them on line to obtain our line 2.
It represents the parabola opening upward with vertices (1,-4)Let us mark few coordinates so that we may graph the parabola.i) x=0 ; ; (0,-3)ii)x=-1 ; ; (-1,0)iii) x=2 ; ;(2,-3)iii) x=1 ; ;(1,-4)iii) x=-2 ; ;(-2,5)Now we plot them on coordinate axis and line them to form our parabolaWhen we plot them we see that we have two coordinates (2,-3) and (-2,5) are common , on which our graphs are intersecting. These coordinates are solution to the two graphs.
Question 1 1.1. Express each of the ratios below in the simplest form. Show all you steps and calculations. 1.1.1. 75: 125 1.1.2. 3mm: 3m 1.1.3. 7500g: 2 Kg 1.1.4.250ml: 21 1.1.5. 250 kg: 2 tonnes bank fo
Answers
The ratio of 75:125 is 3:5.
The ratio 3 mm : 3000 mm is 1:1000.
The ratio of 7500g:2 Kg is 3.75:1.
The ratio of 250ml:2l is 1:8.
How to calculate the ratioTo simplify this ratio, we need to find the greatest common factor (GCF) of 75 and 125, and divide both terms by it.
The factors of 75 are: 1, 3, 5, 15, 25, 75.
The factors of 125 are: 1, 5, 25, 125.
The GCF is 25.
Dividing both terms by 25, we get:
75 ÷ 25 = 3
125 ÷ 25 = 5
Therefore, the simplified ratio is 3:5.
1.1.2. 3mm:3m
To simplify this ratio, we need to convert the units so that they are the same.
1 m = 1000 mm
So, 3 m = 3000 mm
Now, the ratio is 3 mm : 3000 mm.
We can simplify this ratio by dividing both terms by 3:
3 mm ÷ 3 = 1 mm
3000 mm ÷ 3 = 1000 mm
Therefore, the simplified ratio is 1:1000.
1.1.3. 7500g:2 Kg
To simplify this ratio, we need to convert either grams to kilograms or kilograms to grams so that both terms have the same unit.
7500 g = 7.5 kg (since 1 kg = 1000 g)
Now, the ratio is 7.5 kg : 2 kg.
We can simplify this ratio by dividing both terms by 2:
7.5 kg ÷ 2 = 3.75 kg
2 kg ÷ 2 = 1 kg
Therefore, the simplified ratio is 3.75:1.
1.1.4. 250ml:21
To simplify this ratio, we need to convert milliliters to a whole number.
We can convert 250 ml to 250/21 ml by dividing both terms by 21:
250 ml ÷ 21 = 11.9 ml (rounded to one decimal place)
Now, the ratio is 11.9 ml : 21.
We can simplify this ratio by dividing both terms by 0.1:
11.9 ml ÷ 0.1 = 119 ml
21 ÷ 0.1 = 210
Therefore, the simplified ratio is 119:210.
1.1.5. 250 kg:2 tonnes
To simplify this ratio, we need to convert either kilograms to tonnes or tonnes to kilograms so that both terms have the same unit.
1 tonne = 1000 kg
So, 2 tonnes = 2000 kg
Now, the ratio is 250 kg : 2000 kg.
We can simplify this ratio by dividing both terms by 250:
250 kg ÷ 250 = 1 kg
2000 kg ÷ 250 = 8 kg
Therefore, the simplified ratio is 1:8.
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The table below shows Zoey's earnings on the job.
Time (hours)
Time (hours)
Earnings (dollars)
Earnings (dollars)
3
3
$
86.10
$86.10
11
11
$
315.70
$315.70
24
24
$
688.80
$688.80
What is the constant of proportionality between earnings and time in hours?
Answers
Answer: 11 and more
Step-by-step explanation:
8. Effect size - Cohen's d and r squared An industrial/organizational psychologist has been consulting with a company that runs weekend job-seeking workshops for the unemployed. She collected data on several issues related to these workshops and, after conducting statistical tests, obtained statistically significant findings. She needs to find a way to evaluate effect size so that she can make recommendations to the company. One of the psychologist’s findings is that one year after the workshop, a sample of 49 job seekers who received training on setting career goals scored an average of 6.5 as measured on a 9-point job-search satisfaction scale, with a standard deviation of 1.2. The typical job seeker scores 5.8 points. The psychologist finds that the estimated Cohen’s d is , the t statistic is 4.12, and r² is . Using Cohen’s d and Cohen’s guidelines for interpreting the effect size with the estimated Cohen’s d, there is a treatment effect. Using r² and the extension of Cohen’s guidelines for interpreting the effect size using r², there is a treatment effect. (Hint: When using Cohen’s guidelines for interpreting the effect size, if the value lies between two categories, then specify the range covered by both categories, for example, medium to large.) Another one of the psychologist’s findings is that a sample of 144 job seekers who received training on identifying marketable skills worked more than 30 hours an average of 6.9 months in the last year, with a standard deviation of 2.5. The typical job seeker works 6.4 months. She finds that the estimated Cohen’s d is , the t statistic is 2.38, and r² is . Using Cohen’s d and Cohen’s guidelines for interpreting the effect size with the estimated Cohen’s d, there is a treatment effect. Using r² and the extension of Cohen’s guidelines for interpreting the effect size with r², there is a treatment effect.
Answers
For the first finding on job-search satisfaction scale, the estimated Cohen’s d is not provided in the question. However, assuming that it is provided in the actual data, the psychologist can use Cohen’s guidelines for interpreting the effect size based on the estimated Cohen’s d. According to Cohen’s guidelines, an effect size of 0.2 is considered small, 0.5 is considered medium, and 0.8 or higher is considered large. Therefore, the psychologist needs to compare the estimated Cohen’s d with these values to evaluate the effect size.
For the second finding on the number of months worked in the last year, the estimated Cohen’s d is also not provided in the question. The psychologist can use the same approach to evaluate the effect size using Cohen’s guidelines based on the estimated Cohen’s d.
Alternatively, the psychologist can also use r² as a measure of effect size. R² represents the proportion of variance in the outcome variable that is explained by the treatment or intervention. According to Cohen’s guidelines for r², an effect size of 0.01 is considered small, 0.09 is considered medium, and 0.25 or higher is considered large. Therefore, the psychologist can compare the estimated r² with these values to evaluate the effect size.
Based on the information provided, both findings show statistically significant results with treatment effects. However, the actual effect sizes cannot be evaluated without the estimated Cohen’s d or r² values.
Effect size for job-search satisfaction is Cohen's d = 0.7, t statistic = 4.12 and r² = 0.49.
According to Cohen's guidelines, a Cohen's d of 0.7 is considered a large effect size. This means that the workshop had a significant impact on the job-search satisfaction of the participants. The t statistic of 4.12 is also significant, indicating that the difference between the workshop participants and the control group is unlikely to have occurred by chance. The r² of 0.49 indicates that the workshop accounted for 49% of the variance in job-search satisfaction.
Effect size for months worked
Cohen's d = 0.36
t statistic = 2.38
r² = 0.13
According to Cohen's guidelines, a Cohen's d of 0.36 is considered a medium effect size. This means that the workshop had a significant impact on the number of months worked by the participants. The t statistic of 2.38 is also significant, indicating that the difference between the workshop participants and the control group is unlikely to have occurred by chance. The r² of 0.13 indicates that the workshop accounted for 13% of the variance in months worked.
Interpretation
Both of the effect sizes found by the psychologist are significant, indicating that the workshops had a positive impact on the job-search satisfaction and the number of months worked by the participants. The effect size for job-search satisfaction is larger than the effect size for months worked, suggesting that the workshop had a greater impact on job-search satisfaction than on the number of months worked.
Conclusion
The psychologist's findings suggest that the workshops had a positive impact on the job-search satisfaction and the number of months worked by the participants. The effect sizes for both outcomes are significant, and the effect size for job-search satisfaction is larger than the effect size for months worked. These findings suggest that the workshops may be an effective way to help unemployed people find jobs.
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